ON A FRACTIONAL SCHRODINGER EQUATION IN THE PRESENCE OF HARMONIC POTENTIAL

被引：2

作者：

Ding, Zhiyan ^{[1
]}

Hajaiej, Hichem ^{[2
]}

机构：

[1] Univ Wisconsin Madison, Dept Math, Madison, WI 53706 USA

[2] Calif State Univ Los Angeles, Dept Math, Los Angeles, CA 90032 USA

来源：

ELECTRONIC RESEARCH ARCHIVE | 2021年 / 29卷 / 05期

关键词：

Schrodinger equation; fractional Laplacian; harmonic potential; stand-ing waves; variational methods; STANDING WAVES; VARIATIONAL APPROACH; ORBITAL STABILITY; INEQUALITIES;

D O I：

10.3934/era.2021047

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we establish the existence of ground state solutions for a fractional Schrodinger equation in the presence of a harmonic trapping potential. We also address the orbital stability of standing waves. Additionally, we provide interesting numerical results about the dynamics and compare them with other types of Schrodinger equations [11, 18]. Our results explain the effect of each term of the Schrodinger equation: the fractional power, the power of the nonlinearity, and the harmonic potential.

引用

页码：3449 / 3469

页数：21

共 50 条

[11] Local smoothing effect on the Schrodinger equation with harmonic potential
Fang, Daoyuan
Han, Zheng
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2014, 409 (01) : 28 - 40
[12] The nonlinear Schrodinger equation with a strongly anisotropic harmonic potential
Ben Abdallah, N
Méhats, F
Schmeiser, C
Weishäupl, RM
[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2005, 37 (01) : 189 - 199
[13] A generalized time fractional Schrodinger equation with signed potential
Sun, Rui
Deng, Weihua
[J]. COMMUNICATIONS IN ANALYSIS AND MECHANICS, 2024, 16 (02): : 262 - 277
[14] An algorithm for fractional Schrodinger equation in case of Morse potential
Al-Raeei, Marwan
E-Daher, Moustafa Sayem
[J]. AIP ADVANCES, 2020, 10 (03)
[15] Fractional Schrodinger equation for a particle moving in a potential well
Luchko, Yuri
[J]. JOURNAL OF MATHEMATICAL PHYSICS, 2013, 54 (01)
[16] Bound state for the fractional Schrodinger equation with unbounded potential
Cheng, Ming
[J]. JOURNAL OF MATHEMATICAL PHYSICS, 2012, 53 (04)
[17] THE FRACTIONAL SCHRODINGER EQUATION WITH SINGULAR POTENTIAL AND MEASURE DATA
Gomez-Castro, David
Luis Vazquez, Juan
[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2019, 39 (12) : 7113 - 7139
[18] VARIATIONS ON THE LINEAR HARMONIC OSCILLATOR: FOURIER ANALYSIS OF A FRACTIONAL SCHRODINGER EQUATION
Bezak, Viktor
[J]. REPORTS ON MATHEMATICAL PHYSICS, 2019, 84 (03) : 269 - 288
[19] Multilinear Eigenfunction Estimates for the Harmonic Oscillator and the Nonlinear Schrodinger Equation with the Harmonic Potential
Akahori, Takafumi
Ito, Kenichi
[J]. ANNALES HENRI POINCARE, 2009, 10 (04): : 673 - 709
[20] Fractional Schrodinger equation
Laskin, N
[J]. PHYSICAL REVIEW E, 2002, 66 (05): : 7 - 056108

← 1 2 3 4 5 →